Question

if sin theta + cos theta= x, then show that tan theta + cot theta = 2/x^2-1

Answer 1

Answer is in the above attachment

Hope u like it

Please like and mark Brainliest

Answer 2

$\tan \theta+\cot \theta =\dfrac{2}{x^2-1}$, shown.

Step-by-step explanation:

We have,

$\sin \theta +\cos \theta= x$

Show that $\tan \theta+\cot \theta =\dfrac{2}{x^2-1}$.

$\sin \theta +\cos \theta= x$

Squaring both sides, we get

$(\sin \theta +\cos \theta)^2= x^2$

⇒ $\sin^2 \theta +\cos^2 \theta+2\sin \theta \cos \theta= x^2$

⇒ $1+2\sin \theta \cos \theta= x^2$

Using the trigonometric identity,

$\sin^2 A +\cos^2 A=1$

⇒ $\sin \theta \cos \theta= \dfrac{x^2-1}{2}$                     ........... (1)

L.H.S. $=\tan \theta+\cot \theta$

$=\dfrac{\sin \theta}{\cos \theta} +\dfrac{\cos \theta}{\sin \theta}$

$=\dfrac{\sin^2 \theta+\cos^2 \theta}{\sin \theta\cos \theta}$

$=\dfrac{1}{\sin \theta\cos \theta}$

Using equation (1), we get

$=\dfrac{1}{\dfrac{x^2-1}{2}}$

$=\dfrac{2}{x^2-1}$

= L.H.S., shown.